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Simplifying (5n + 4)(n + -2) = 0 Reorder the terms: (4 + 5n)(n + -2) = 0 Reorder the terms: (4 + 5n)(-2 + n) = 0 Multiply (4 + 5n) * (-2 + n) (4(-2 + n) + 5n * (-2 + n)) = 0 ((-2 * 4 + n * 4) + 5n * (-2 + n)) = 0 ((-8 + 4n) + 5n * (-2 + n)) = 0 (-8 + 4n + (-2 * 5n + n * 5n)) = 0 (-8 + 4n + (-10n + 5n2)) = 0 Combine like terms: 4n + -10n = -6n (-8 + -6n + 5n2) = 0 Solving -8 + -6n + 5n2 = 0 Solving for variable 'n'. Factor a trinomial. (-4 + -5n)(2 + -1n) = 0Subproblem 1
Set the factor '(-4 + -5n)' equal to zero and attempt to solve: Simplifying -4 + -5n = 0 Solving -4 + -5n = 0 Move all terms containing n to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -5n = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -5n = 0 + 4 -5n = 0 + 4 Combine like terms: 0 + 4 = 4 -5n = 4 Divide each side by '-5'. n = -0.8 Simplifying n = -0.8Subproblem 2
Set the factor '(2 + -1n)' equal to zero and attempt to solve: Simplifying 2 + -1n = 0 Solving 2 + -1n = 0 Move all terms containing n to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1n = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1n = 0 + -2 -1n = 0 + -2 Combine like terms: 0 + -2 = -2 -1n = -2 Divide each side by '-1'. n = 2 Simplifying n = 2Solution
n = {-0.8, 2}
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